For the following system: G(s) =(s+ 2)/ (s+5)(s+9) (a) (5 points) Determine the controllability of the system. (b) (10 points) Design a state feedback controller by placing the poles for a second order system ap- proximation with damping ratio,?=.7, and natural frequency of?n= 96. [Do not use the Matlab functions place or acker] (c) (5 points) Simulate your system in (b) using both matlab and Simulink and show the step response.
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